Research
interests : Nonlinear Dynamical Systems and their applications in
Biology (Mathematical Neuroscience and Computational Toxicology)
I
study the spatio-temporal dynamics of complex
systems coming from the mathematical modeling of biological
systems. My approach is to use computer simulations and to
develop
mathematical
tools coming from the theory of nonlinear differential equationsanddiscrete equations. In the context
of
computational neuroscience I
mainly focus on excitable media and neural networks. The goal
of this research is twofold: first to understand information processing
in the brain and the
neuronal coding of information from a single nerve cell to large
network
of neurons. My activities in computational toxicology focus on
physiologically based pharmacokinetics models.
My general areas of
research
interest
are in
Dynamics of Neural Systems.
Mathematical modelling in biology.
Nonlinear
oscillations, bifurcations and
synchronization.
Intermediate
report for the SNF. In
collaboration with E. de
Lange, I. Belykh, M. Hasler,
R. Jolivet and W. Gerstner (2002).
J. Demongeot, J.Aracena, S. Ben
Lamine, S.
Meignen, A. Tonnelier and R. Thomas, Dynamical systems and biological
regulations, Complex Systems (2001), pp.105-149.
A. Tonnelier and P. Cinquin. Optimal
control for matching and
segmentation (1999).
Phd-Thesis :
(in
french) Nonlinear
dynamic and bifurcations
in mathematical neuroscience. (File
.ps.gz), (File
.ps) (Thèse
de Mathématiques
Appliquées
l'Université Joseph Fourier, Grenoble, 2001).